The following examples are from Lasnik, Howard. 2001, "When Can You Save a Structure by Destroying It?" NELS 31: 301-320, and these appear to pose a problem for the proposal in Fukaya 2003. We will try to address the relevant issues under this posting.

(1) a. (= Lasnik 2001: (51))
Every linguist_i met a philosopher who criticized some of his_i work, but I'm not sure how much of his_i work [every linguist_i met a philosopher who criticized t]
b. (= Lasnik 2001: (52))
Every linguist_i met a philosopher who criticized some of his_i work.
Tell me how much of his_i work [every linguist_i met a philosopher who criticized t]

(2) a. (= Lasnik 2001: (53))
??Every linguist_i met a philosopher who criticized some of his_i work, but I'm not sure how much of his_i work the philosopher criticized t
b. (= Lasnik 2001: (54))
?*Every linguist_i met a philosopher who criticized some of his_i work.
Tell me how much of his_i work the philosopher criticized t.

(3) a. (= Lasnik 2001: (55))
Each of the linguists met a philosopher who criticized some of the other linguists, but I'm not sure how many of the other linguists
b. (= Lasnik 2001: (56))
?*How many of the other linguists did the philosopher criticize